And Hashem spoke to Moshe in the wilderness of Sinai in the Ohel Moed in the second month of the second year of their exodus from Egypt saying: Take a tally of the entire congregation of Bnai Yisrael according to their families (and) their household of their father according to the number of names. (Count) every male head. (Sefer BeMidbar 1:1-2)
1. Moshe and the leaders of the shevatim take a census of the nation
The above passages introduce Sefer BeMidbar. In these passages, Hashem instructs Moshe to conduct a census of the males of Bnai Yisrael. This census will not only determine the adult male population of the entire nation but also the adult male population of each shevet – tribe. In the subsequent passages Hashem instructs Moshe to enlist the cooperation of the heads of the tribes. The census is to be conducted under the auspices of this entire group of leaders. In the course of the Torah’s account of the census and its results, the tribes are enumerated three times. In each instance the enumeration has its own unique characteristics and apparent quirks.
Before considering and analyzing these enumerations it will be useful to review three basic issues:
• Each of Yaakov’s children was the patriarch of his own shevet. However, there is one exception to this rule. Yosef’s two sons – Ephraim and Menashe – were each patriarchs of their own shevet. Therefore, although Yaakov had twelve sons, there are thirteen shevatim. Eleven of his sons served as patriarchs for their own shevet. Yosef’s sons served as patriarchs for two additional tribes.
• In the census that Moshe is instructed to conduct, one tribe – Leyve – is to be excluded. Hashem instructs Moshe to conduct a separate census of Shevet Leyve. In other words, Moshe was instructed to conduct one census of twelve tribes and a separate census of Shevet Leyve.
• Yaakov’s sons were born from four wives. Leyah gave birth to six sons and Rachel gave birth to two. The remaining four sons were the children of “surrogate” wives. During the period that she was childless, Rachel gave her servant Bilhah to Yaakov as a surrogate for herself. Bilhah gave birth to two sons. Leyah also experienced a period during which she could not conceive and she followed her sister Rachel’s example. She gave her servant Zilpah to Yaakov as her surrogate and she gave birth to two sons.
The following table presents the birth order of Yaakov’s sons and identifies each son’s mother.
And these are the names of men that should stand with you: For Reuven – Elitzur ben Sheteyur. (Sefer BeMidbar 1:5)
2. The first listing of the shevatim
Hashem instructs Moshe to conduct the census with the participation of the heads of the shevatim. Hashem identifies by name the head of each shevet. This is the first time the shevatim are enumerated in the parasha. The order in which the tribes are identified is as follows:
The table above divides the shevatim into three groups each composed of four tribes. This division into groups reflects the Torah’s cantilations – the traditional tune to which the passages are read. It is immediately observable that the order in which the shevatim are listed is not the birth order of their patriarchs. What is the basis of the order?
Apparently, the groups are – in part – determined by aesthetic considerations. Each leader and his shevet are identified in their own passage. Rather than listing of the twelve leaders and tribes a continuous series of twelve passages, the twelve passages are divided into three smaller groups – each composed of four passages. The listing begins with the sons of Leyah. These are listed in their birth order. Next the sons of Rachel are listed in their birth order. Finally, the sons of the two surrogates are listed. Among the sons of the surrogates, the oldest son – Dan – is listed first. However, the remaining sons are not listed in birth order or in any apparent order. There are three important elements of this first listing:
• The shevatim descendant from the sons of Leyah and Rachel are given precedence over those of the surrogate wives and the shevatim descendant from Leyah’s sons are placed before those from Rachel’s sons.
• The order of the shevatim descendant from Leyah and Rachel reflects the birth orders of their patriarchs.
• The order of shevatim descendant from the surrogates is not as strictly determined by birth order. Dan is recognized as eldest but birth order plays no further role in the listing of these tribes.
And it was that the descendants of Reuven the firstborn of Yisrael – their descendants according to their families (and ) the household of their father – according to the number of names corresponding with all of the individual males twenty years of age or above, every one (fit) to go forth in legion. The census for the tribe of Reuven was forty-six thousand five hundred. (Sefer BeMidbar 1:20-21)
3. The second listing of the shevatim
The above two passages are difficult to render into conventional English but their message is simple. They are the first passages of the second listing of the shevatim. These passages initiate the report of the census of Bnai Yisrael and reveal that Shevet Reuven – the tribe of Reuven included 46,500 males over age twenty. In the ensuing passages the Torah reports the census for each tribe. The order in which the censuses of the tribes are reported is as follows:
The order in which the censuses of the tribes are reported is virtually identical to the order followed in the first list. The “Leyah shevatim” come first and are listed in birth order of their patriarchs. The “Rachel shevatim” follow. These are also listed according to the birth order of their patriarchs. Finally the tribes descendant from the surrogates are listed. Dan – descendant from the oldest of the surrogates’ sons – is listed first. Birth order is ignored in listing the remaining members of this group. However, there is odd deviation from this order. In this list, Gad – descendant from a surrogate – is inserted in the middle of the tribes descendant from Leyah. How can this placement of Gad be explained?
And Hashem spoke to Moshe and to Aharon saying: Each man of Bnai Yisrael should camp according to the banner (with) the sign for the household of their father. (Camp) at a distance surrounding the Ohel Moed.” (Sefer BeMidbar 2:1-2)
4. The third listing of the shevatim
These passages introduce the third listing of the tribes in the parasha. Hashem explains to Moshe and Aharon that Bnai Yisrael are to encamp according to a specific plan. The shevatim are to assigned positions surrounding the Mishcan. Each shevet must encamp in its specific assigned locations. Three shevatim are assigned to each side of the Mishcan. Within each of these four groups of tribes one tribe is assigned a lead role and the other three are placed under the banner of the lead shevet. The following table describes the order in which the tribes are listed, the position of each tribe relative to the Mishcan, and the lead tribe in each group is identified:
This third listing of the shevatim utilizes the same order as the second listing. Again, Gad is inserted among the shevatim descendant from Leyah. Rabbaynu Avraham ibn Ezra suggests that if the context of this final listing is considered, the order it employs can be easily explained.
As explained above, this listing places each shevet in its assigned position surrounding the Mishcan. Therefore, in order to understand the sequence of shevatim in this list, it is essential to identify the criteria by which the shevatim were assigned positions and placed in groups.
One issue that is immediately evident is that the groupings were not designed to create four equally sized camps or groups. Yehudah’s camp was much larger than any other. It included 186,400 men. Ephraim’s was the smallest with 108,100 male members. So, if numerical equivalency was not important, on what basis were the groups formed?
Ibn Ezra suggests that the following considerations determined the groups and the order employed in the listing of the tribes:
• All groups include the same number of tribes. Each group consists of the lead tribe and two additional members.
• The groups preserve the fraternal relationship between the tribes. Preserving this fraternal relationship presents two problems. First, there are five “Leyah shevatim”. These are too many shevatim for a single group and not enough for two groups. Second, there are four “surrogate shevatim”. These also are too many for a single group and too few for two groups. This problem is solved by joining one of the “surrogate shevatim” to the Reuven group. The selected shevet is Gad. Gad was the oldest son of Zilpah – Leyah’s surrogate. Therefore, Gad has the strongest fraternal relationship with the “Leyah shevatim”. The inclusion of Gad in the Reuven group, leaves three remaining “surrogate shevatim”. These form the northern Dan group.
• Leadership of each group is awarded on the basis of a specific characteristic of the leader shevet. Reuven was Yaakov’s firstborn son. His shevet is assigned leadership of the southern group. Yaakov blessed his sons before his death. In these blessings he promised Yehudah that the future leadership of Bnai Yisrael would descend from him. Therefore, Yehudah is assigned leadership of the eastern group. Yaakov also blessed Yosef’s sons and he assigned greater status to Ephraim. Ephraim is leader of the western group. Dan was the eldest son of the surrogates. Therefore, Dan is assigned leadership of the northern group.
These factors determine the construction of the four groups. The order in which the groups are listed and the order in which the tribes within each group are listed is determined by the same criteria employed in the parasha’s initial list. The two “Leyah shevatim” groups are listed first. The members in each group are listed according to birth order – with Gad inserted as the third member of the Reuven group. The “Rachel shevatim” group appears second. The “surrogate shevatim” group appears last. Dan is given precedence but birth order among the remaining members is ignored.
Finally, ibn Ezra explains that the order used in the second list in the parasha is adopted from the third list. The second list reported the censuses for each tribe. Apparently this was a preparatory step to the assignment of the shevatim to their respective groups and positions. The preparatory nature of this report is alluded to through the adoption of the order used in the third list.
In short, the initial listing of the shevatim provides a basic set of principle that is employed in the other listings. This initial listing does not follow the birth order of the patriarchs of the shevatim. Instead the shevatim are listed based upon a matriarchal scheme. Birth order plays only a secondary role.
The second and the third listings employ the same principles as the first listing. However, these listings deviate from the initial listing because of contextual considerations. These listing are associated with the assignment of shevatim to groups and camps surrounding the Mishcan. This requires that Gad be inserted among the “Leyah tribes” after Shimon.
 Rabbaynu Avraham ibn Ezra, Commentary on Sefer BeMidbar, 1:20-43.